Heres the modified wiring diagram.
1N4001 = 1 amp diode. The diode has a silver band on it. You want to install it, so that the end with the silver band faces away from the relay. In other words the end with the silver band connects to the door trigger wire.
The diode will eliminate feedback into the door trigger circuit when 85 on the relay is manually triggered by using the switch. Diodes only allow current to flow one way.
Switch tied to constant +12V is the master switch. If its off, the entire circuit is dead.
This is how the circuit works:
1. Constant +12V in on position and switch on 85 in off position = cathodes will turn on whenever any door is open. When all doors are closed, cathodes will be off.
2. All doors closed. Switch on 85 in on position = cathodes turn on and stay on until you flip the switch to the off position. The switch tied to constant +12V must also be on, since its the master switch for the entire circuit.
3. Switch tied to constant +12V in off position = entire circuit is dead regardless if any door is open or all doors are closed. And the other switch has no effect.